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auto | NAV::math::bilinearInterpolation (const auto &tx, const auto &ty, const auto &c00, const auto &c10, const auto &c01, const auto &c11) |
| Bilinear interpolation.
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double | NAV::math::calcEllipticalIntegral (double phi, double m) |
| Calculates the incomplete elliptical integral of the second kind.
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template<std::floating_point T> |
T | NAV::math::csc (const T &x) |
| Calculates the cosecant of a value (csc(x) = sec(pi/2 - x) = 1 / sin(x))
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template<typename Derived> |
Derived::PlainObject | NAV::math::expm (const Eigen::MatrixBase< Derived > &X, size_t order) |
| Calculates the state transition matrix 𝚽 limited to specified order in 𝐅𝜏ₛ
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uint64_t | NAV::math::factorial (uint64_t n) |
| Calculates the factorial of an unsigned integer.
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template<std::integral Out, size_t Bits, std::integral In> |
constexpr Out | NAV::math::interpretAs (In in) |
| Interprets the input integer with certain amount of Bits as Output type. Takes care of sign extension.
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template<typename Derived> |
Derived::PlainObject | NAV::math::inverseSqrt (const Eigen::MatrixBase< Derived > &matrix) |
| Returns the inverse square root of a matrix.
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template<typename Derived> |
Derived::PlainObject | NAV::math::lerp (const Eigen::MatrixBase< Derived > &a, const Eigen::MatrixBase< Derived > &b, auto t) |
| Linear interpolation between vectors.
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LerpSearchResult | NAV::math::lerpSearch (const auto &data, const auto &value) |
| Searches the value in the data container.
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template<typename Derived> |
std::optional< std::pair< Eigen::Matrix< typename Derived::Scalar, Derived::RowsAtCompileTime, Derived::ColsAtCompileTime >, Eigen::Vector< typename Derived::Scalar, Derived::RowsAtCompileTime > > > | NAV::math::LtDLdecomp_choleskyFact (const Eigen::MatrixBase< Derived > &Q) |
| Find (L^T D L)-decomposition of Q-matrix via a backward Cholesky factorization in a bordering method formulation.
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template<typename Derived> |
std::optional< std::pair< Eigen::Matrix< typename Derived::Scalar, Derived::RowsAtCompileTime, Derived::ColsAtCompileTime >, Eigen::Vector< typename Derived::Scalar, Derived::RowsAtCompileTime > > > | NAV::math::LtDLdecomp_outerProduct (const Eigen::MatrixBase< Derived > &Qmatrix) |
| Find (L^T D L)-decomposition of Q-matrix via outer product method.
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double | NAV::math::normalCDF (double value) |
| Calculates the cumulative distribution function (CDF) of the standard normal distribution.
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template<std::floating_point T> |
constexpr T | NAV::math::round (const T &value, size_t digits) |
| Round the number to the specified amount of digits.
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template<std::floating_point T> |
constexpr T | NAV::math::roundSignificantDigits (T value, size_t digits) |
| Round the number to the specified amount of significant digits.
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template<std::floating_point T> |
T | NAV::math::sec (const T &x) |
| Calculates the secant of a value (sec(x) = csc(pi/2 - x) = 1 / cos(x))
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template<typename T> |
int | NAV::math::sgn (const T &val) |
| Returns the sign of the given value.
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template<typename T> |
T | NAV::math::sign (const T &x, const T &y) |
| Change the sign of x according to the value of y.
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template<typename Derived> |
Eigen::Matrix< typename Derived::Scalar, 3, 3 > | NAV::math::skewSymmetricMatrix (const Eigen::MatrixBase< Derived > &a) |
| Calculates the skew symmetric matrix of the given vector. This is needed to perform the cross product with a scalar product operation.
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template<typename Derived> |
Eigen::Matrix< typename Derived::Scalar, 3, 3 > | NAV::math::skewSymmetricMatrixSquared (const Eigen::MatrixBase< Derived > &a) |
| Calculates the square of a skew symmetric matrix of the given vector.
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template<typename DerivedA, typename DerivedQ> |
DerivedA::Scalar | NAV::math::squaredNormVectorMatrix (const Eigen::MatrixBase< DerivedA > &a, const Eigen::MatrixBase< DerivedQ > &Q) |
| Calculates the squared norm of the vector and matrix.
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Simple Math functions.
- Author
- T. Topp (topp@.nosp@m.ins..nosp@m.uni-s.nosp@m.tutt.nosp@m.gart..nosp@m.de)
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N. Stahl (HiWi: Elliptical integral)
- Date
- 2023-07-04
Definition in file Math.hpp.